To convert the base-6 number \( 45113_6 \) to a base-10 (decimal) number, follow these steps:

### Step 1: Write the base-6 number in expanded form.
Each digit represents a power of 6, starting from the rightmost digit (which is \(6^0\)).

\[
45113_6 = 4 \cdot 6^4 + 5 \cdot 6^3 + 1 \cdot 6^2 + 1 \cdot 6^1 + 3 \cdot 6^0
\]

### Step 2: Calculate the powers of 6.
\[
6^0 = 1,\quad 6^1 = 6,\quad 6^2 = 36,\quad 6^3 = 216,\quad 6^4 = 1296
\]

### Step 3: Multiply the digits by the powers of 6 and sum the results.
\[
45113_6 = (4 \cdot 1296) + (5 \cdot 216) + (1 \cdot 36) + (1 \cdot 6) + (3 \cdot 1)
\]
\[
= 5184 + 1080 + 36 + 6 + 3
\]
\[
= 6309
\]

Thus, \( 45113_6 \) in base-10 is:
\[
45113_6 = 6309_{10}
\]

### Final Answer:
\[
(45113)_6 = (6309)_{10}
\]

Would you like further details or explanations? 

Here are 5 related questions to consider:
1. How would you convert a base-10 number to base-6?
2. Can you explain why each position in base-6 is a power of 6?
3. How would this process change for other bases, like base-8 or base-12?
4. What are some practical applications of base conversions?
5. How would you convert fractional numbers from base-6 to base-10?

**Tip:** Always double-check the powers and multiplications when converting between bases to avoid small errors!

Learn how to convert the base-6 number (45113)_6 to base-10 with step-by-step instructions. This problem covers key concepts of number systems and base conversion, including the use of powers of 6. Suitable for students in Grades 7-10.

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